{"id":"ffcb0e7d-4d18-43b2-aaf0-6f172e6ad2c2","arxiv_id":"2507.03939","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":2.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Three wormhole models are constructed in linear f(Q) gravity using varying Chaplygin, generalized Chaplygin, and varying barotropic equations of state, all of which violate the null energy condition at the throat.","lead":"This paper constructs three traversable wormhole solutions in a linear f(Q) gravity model by assuming dark energy equations of state for the radial pressure. The models are shown to violate the null energy condition at the throat, a standard requirement for traversable wormholes.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"For the generalized Chaplygin model, Eq. (5.7) with the paper's own parameters a=-1.2 is not asymptotically flat: b(r)/r grows roughly as r^2, so the paper's claim that all three shape functions satisfy Morris-Thorne conditions is false.","rationale":"The reader's rejection is well supported by the undisclosed overlap with earlier f(Q) wormhole papers and by the vacuous TOV analysis (with constant redshift, F_G vanishes and the TOV equation reduces to automatic conservation). However, the most load-bearing problem with the paper's central claim is even more direct: the generalized Chaplygin wormhole, one of the three central constructions, does not satisfy the paper's own asymptotic flatness requirement. This is an internal inconsistency, not a disagreement with external consensus. The algebra for WH2 is decisive: from Eqs. (4.6)-(4.8) and (5.6), the shape function obeys A^(a+1) b (b')^a = B r^(2a+3); a power-law ansatz b ~ r^k yields k = 3 for all a != -1, so b/r diverges. The explicit form (5.7) with a = -1.2 confirms this. Therefore the statement in Section 5.2 that the asymptotic flatness condition is retained is false for WH2, and the later embedding and TOV sections inherit this failure. I therefore keep the reader's REJECT verdict; no change of verdict is needed, but the specific asymptotic-flatness contradiction is a stronger and more precise grounds than the ones the reader emphasized.","tokens_in":16448,"tokens_out":17391,"duration_ms":174815,"concrete_test":"Recompute b(r)/r from Eq. (5.7) at r = 10, 100, and 1000 using a = -1.2, B = 1, c1 = 10, and alpha = -0.5; if the ratio grows as roughly r^2 instead of tending to zero, WH2 fails asymptotic flatness. As an independent check, substitute b(r) = K r^3 into the differential equation A^(a+1) b (b')^a = B r^(2a+3) derived from Eqs. (4.6)-(4.8) and (5.6), and verify that it is an exact late-time solution, confirming that the non-flat behavior is structural rather than a plotting artifact.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires every shape function to obey the Morris-Thorne asymptotic flatness condition b(r)/r -> 0 as r -> infinity, stated in Section 3. For model WH2, Eq. (5.7) with a = -1.2 gives an exponent a/(a+1) = 6 and a radial power r^(3/a+3) = r^(1/2), so b(r) = [D r^(1/2) + C]^6 ~ D^6 r^3. Consequently b(r)/r ~ r^2 -> infinity, not zero. This is not a parameter-choice issue: substituting b ~ r^k into the linear f(Q) equations with EoS (5.6) gives k + a(k-1) = 2a + 3, hence k = 3 for every a != -1. Thus the generalized Chaplygin EoS (5.6) cannot produce an asymptotically flat wormhole in this model at all. The text in Section 5.2 claims flatness is retained, and Fig. 4 labels b/r -> 0, but the formula itself and the plotted numerical range contradict that claim. Since WH2 is one of the paper's three central traversable-wormhole constructions, the paper's central claim fails on its own stated criteria.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper constructs static, spherically symmetric Morris-Thorne wormhole solutions in linear f(Q) gravity with a constant redshift function. Three dark-energy equations of state are imposed on the radial pressure: varying Chaplygin gas (Eq. 5.1), generalized Chaplygin gas (Eq. 5.6), and varying barotropic fluid (Eq. 6.1). Exact shape functions b(r) are presented for each case, followed by graphical checks of the throat, flaring-out, and asymptotic flatness conditions; energy-condition plots; embedding diagrams; and a TOV-equation force balance. The abstract and conclusion claim that all three models satisfy the Morris-Thorne conditions, violate the NEC, and are therefore traversable wormholes.","tokens_in":16629,"tokens_out":17614,"duration_ms":195430,"significance":"The paper is an example-based study in an active area: exact wormhole solutions in modified gravity with dark-energy fluids. The field equations for the linear f(Q) model are standard, and the strategy of imposing an equation of state on p_r is a common and legitimate way to close the underdetermined system. If the solutions were correct, they would provide a set of explicit shape functions and energy-condition profiles worth comparing with earlier f(Q) wormhole literature. However, the generalized Chaplygin model (WH2) fails the asymptotic flatness condition algebraically and in its own figures, the TOV 'stability' test is an identity rather than a stability analysis, and the parameter values for WH3 are internally inconsistent. The main traversable-wormhole claim is therefore not established. No machine-checked proofs or reproducible code are provided; all checks are graphical.","major_comments":[{"comment":"The asymptotic flatness claim for WH2 is false. With the stated parameters a=-1.2, B=1, c1=10, one has a/(a+1)=6 and r^{3/a+3}=r^{1/2}, so b(r) as given in Eq. (5.7) behaves as b(r) ~ D^6 r^3 for large r; consequently b(r)/r ~ r^2, which diverges and violates the Morris-Thorne condition b(r)/r -> 0 stated in Section 3. The text in Section 5.2 that 'we retained the asymptotic flatness condition' is contradicted by the formula itself, and Fig. 4 shows b/r increasing to values of order 10 while Fig. 5 shows b-r > 0 and b' ~ 10^10. Moreover, substituting a power-law ansatz b ~ r^k into Eqs. (4.6)-(4.8) with EoS (5.6) forces k=3 for every a ≠ -1, so an asymptotically flat solution of this type does not exist for the generalized Chaplygin gas in this linear f(Q) model. Since WH2 is one of the paper's three central constructions, the main claim that all three models satisfy the conditions for a viable wormhole is invalid.","section":"Sec. 5.2, Eq. (5.7), Figs. 4-5"},{"comment":"The TOV test does not establish stability. Because the redshift function is constant, phi'=0, and Eq. (8.1) reduces to d p_r/dr + (2/r)(p_r - p_t)=0, which is simply the conservation equation for the anisotropic stress-energy tensor and is identically satisfied by the field equations. The plots of F_A and F_H in Fig. 15 therefore show an algebraic identity, not the reaction of the configuration to perturbations or even a nontrivial equilibrium condition. The abstract and Section 9 use this calculation to support the word 'stability'; that support should be removed or replaced by a genuine stability analysis.","section":"Sec. 8, Eqs. (8.1)-(8.2), Fig. 15"},{"comment":"The energy-condition discussion is self-contradictory. Section 5.1 states that the NEC is violated (rho+p_r <= 0, p_r <= 0) and then, in the same paragraph, says 'the solution satisfies all energy conditions.' Section 5.2 says the NEC 'in terms of both pressures remains true even in the locations where the NEC in terms of P_r is broken,' which is not meaningful as written and conflicts with the abstract's claim that every model violates the NEC. Since the NEC violation is the stated physical output of the paper, these statements must be made mutually consistent before the conclusions can be assessed.","section":"Secs. 5.1-5.2 and 6"},{"comment":"The parameter values for WH3 are not reproducible. The text specifies 'omega = 2; c1 = 1' for the solution, but the captions of Figs. 8 and 9 state 'omega = -2 and c1 = 1', and Fig. 14 uses 'omega = -1'. These choices give different functional forms for b(r) in Eq. (6.2), and with omega = -2 and non-integer u, the base of the fractional power is negative for small r, leaving the real-valued shape function undefined unless a branch choice is specified. The paper should state one consistent parameter set and the branch convention used to generate all WH3 figures.","section":"Sec. 6, Eq. (6.2), Figs. 8-10, 14"}],"minor_comments":[{"comment":"The sentence 'Since each wormhole model is shown to violate the NEC, it can be understood that these wormholes are traversable' is logically incomplete: NEC violation is a necessary condition for traversable wormholes in GR-like settings, but it is not sufficient. The paper does not demonstrate the additional traversability requirements (bounded tidal forces, finite crossing time, no horizon).","section":"Abstract and Sec. 9"},{"comment":"The constants c and c1 are used in the shape function and in the expressions for rho, p_r, and p_t, but their definitions are not given before they appear; the text only later sets both to 0.09 for the plots.","section":"Sec. 5.1, Eqs. (5.2)-(5.5)"},{"comment":"Several presentation issues: Eq. (4.4) contains a spurious dot on f_Q, the text around Eq. (4.2) has an apparent typo in the bracketed term, and the embedding-diagram text refers to Figs. 11-12 while the figures are labeled Figs. 13-14 with inconsistent parameter captions.","section":"Secs. 4-7"},{"comment":"The solutions contain fractional powers of negative quantities such as (-1)^{1/a} and alpha^{-1/a-1} for alpha < 0 and non-integer a. The paper does not specify the principal branch or the convention used to make these expressions real in the figures; this should be stated for the exact formulas to be well defined.","section":"Sec. 5.2 and Figs. 6-7"},{"comment":"The paper should state explicitly what is new relative to Refs. [10]-[12], which already treat wormholes in f(Q) gravity with varying Chaplygin gas, generalized Chaplygin gas, and barotropic fluids; the current manuscript does not contain a novelty statement.","section":"Introduction, Refs. [10]-[12]"}],"recommendation":"reject","confidential_remarks":"The generalized Chaplygin model is not a local error: the asymptotic analysis in Sec. 5.2 shows that no asymptotically flat solution exists for this EoS in the linear f(Q) setup, so the WH2 section cannot be repaired by changing parameters or replotting. The overlap with Refs. [10]-[12] is substantial, and the manuscript does not identify its new contribution. The editor may also wish to ask the authors for the code or parameter files used to generate Figs. 4-5, since those figures appear incompatible even with the displayed Eq. (5.7)."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nHere’s the short version: this is a repackaging of earlier f(Q)-wormhole papers, and one of its three models fails on the paper’s own asymptotic-flatness test. Don’t send it to review.\n\nThe useful part: the f(Q) field equations for a constant redshift function are set up correctly, and the algebra that converts each dark-energy EoS into a shape function is straightforward and easy to follow. A reader could use this as a recipe.\n\nThe problems outweigh that. Novelty is essentially nil: the varying Chaplygin gas, generalized Chaplygin gas, and varying barotropic fluid models are the same as in the paper’s own refs [10], [11], and [12], which are earlier f(Q) wormhole papers. The authors never say what is new. The generalized Chaplygin model (WH2) is genuinely wrong: with the stated parameters a=-1.2, the shape function grows as r^3, so b/r → ∞, contradicting the claim of asymptotic flatness. This is not a parameter accident; the field equations plus the EoS force b ~ r^3 for any a ≠ -1. The plotted b/r values in Fig. 4 climb to ~15, which should have been a red flag. The energy-condition discussion is self-contradictory (Section 5.1 says all conditions are satisfied while reporting NEC violation; Section 5.2 claims NEC in both pressures where radial NEC fails). And the TOV analysis is vacuous: with Φ constant, the gravitational force term vanishes and the remaining balance is just the conservation equation, automatically satisfied by any solution.\n\nThe throat and flaring conditions look okay for WH1 and WH3, and the embedding diagrams are a nice touch, but they don’t rescue the paper. Anyone cataloguing f(Q) wormhole examples might skim it, but I wouldn’t cite it and I wouldn’t use it as a reference. It needs a major rewrite to fix WH2 and to justify even incremental novelty.\n\nRecommendation: desk reject, with an invitation to resubmit after correcting the asymptotic issue and clearly stating what, if anything, is new relative to refs [10]-[12].\n\nBest","headline":"Repackaged f(Q) wormhole constructions, one of which fails asymptotic flatness; not worth refereeing.","tokens_in":17260,"tokens_out":5334,"would_cite":false,"duration_ms":53871,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Exact wormhole shape functions can be produced in linear f(Q) gravity from three dark energy equations of state, and each solution satisfies the Morris-Thorne viability conditions while violating the null energy condition at the throat.","keywords":["wormhole","f(Q) gravity","Chaplygin gas","dark energy","shape function","energy conditions","TOV equation","non-metricity"],"falsifier":"Solve $b(r_0)=r_0$ for each shape function—(5.2), (5.7), and (6.2)—using the paper's stated parameters ($a=0.05$, $u=-4$, $B=1$, $c=0.09$ for WH1; $a=-1.2$, $B=1$, $c_1=10$ for WH2; $\\omega=-2$, $c_1=1$ for WH3) and check for a positive real root $r_0$ with $b'(r_0)<1$. If any model has no positive real throat radius or fails the flaring condition at that radius, the claimed traversable wormhole does not exist; separately, evaluating $\\rho+p_r$ at $r_0$ from (5.3)-(5.4), (5.8)-(5.9), and (6.3)-(6.4) would settle the NEC-violation claim.","tokens_in":16163,"feed_emoji":"🕳️","tokens_out":5466,"duration_ms":57984,"temperature":0.7,"pith_summary":"This paper tries to show that traversable wormholes can be built inside linear f(Q) gravity—a theory of gravity based on non-metricity rather than curvature—by letting the wormhole's radial pressure follow three dark energy equations of state: a varying Chaplygin gas, a generalized Chaplygin gas, and a varying barotropic fluid. For each case the authors derive an exact shape function $b(r)$, check the Morris-Thorne throat, flaring-out, and asymptotic-flatness conditions, and plot the energy conditions. In all three models the null energy condition fails at the throat, which is the standard signal of the exotic matter needed for a traversable wormhole. They also use the Tolman-Oppenheimer-Volkoff balance to argue that the configurations are stable under hydrostatic and anisotropic forces. If true, the result would give a concrete recipe: choose a dark energy equation of state, solve for $b(r)$, and get a wormhole geometry in this modified gravity.","feed_headline":"Dark energy equations of state build traversable wormholes","feed_subtitle":"Exact shape functions satisfy throat, flaring, and flatness conditions while violating the null energy condition.","key_machinery":"The central object is the Morris-Thorne shape function $b(r)$ in the static wormhole line element. Together with a constant redshift function and the linear $f(Q)=\\alpha Q$ Lagrangian, it turns the f(Q) field equations into simple relations: $-\\alpha b'/r^2=\\rho$, $\\alpha b/r^3=p_r$, and $(\\alpha/2)(b'/r^2-b/r^3)=p_t$. The argument works by choosing the radial pressure to obey a dark energy equation of state, solving the resulting differential equation for $b(r)$, and then checking the geometric and energy conditions.","core_discovery":"Within a linear model $f(Q)=\\alpha Q$ with constant redshift function, the paper claims that the field equations reduce to three algebraic relations linking the shape function to energy density and pressures. Substituting the dark energy equations of state $p_r=-B b(r)^u/\\rho^a$, $p_r=-B/\\rho^a$, and $p_r=-\\omega\\rho b(r)^u$ yields closed-form shape functions $b(r)$, and with negative $\\alpha$ these are claimed to meet the throat condition $b(r_0)=r_0$, the flaring condition $b'(r_0)<1$, and asymptotic flatness $b(r)/r\\to 0$. The same solutions are then shown, for chosen parameter values, to give positive energy density but negative radial pressure, so that $\\rho+p_r<0$ at the throat—NEC violation—while the tangential-pressure NEC can still hold in some models. The TOV force balance is plotted and found to vanish, establishing equilibrium.","pith_inferences":["One extension not pursued here is to replace the linear $f(Q)=\\alpha Q$ ansatz with nonlinear f(Q) and ask whether the same equations of state still yield asymptotically flat shape functions, or whether a positive coupling could work.","The hand-picked constants ($B$, $u$, $a$, $\\omega$, $c$) have no independent observational anchor; testing these models would require linking the parameters to cosmological data or to lensing and echo observations of a wormhole candidate.","The throat condition $b(r_0)=r_0$ is checked graphically for the plotted parameters; a numerical root-finding scan over parameter space could reveal whether the models remain traversable away from those values or whether viability is confined to narrow intervals.","Since the redshift is constant, the gravitational redshift signature is absent; a nonzero $\\Phi(r)$ could alter the TOV force balance and the NEC status, so the robustness of the construction under that relaxation is an open question."],"forward_implications":["Each derived shape function is an explicit candidate geometry that can be embedded in three-dimensional space, so the models give visualizable wormhole spacetimes rather than abstract existence statements.","The same construction can be retried with any equation of state: substituting $p_r$ into the relation $\\alpha b/r^3=p_r$ gives a first-order ODE for $b(r)$, so the method is a template for generating new wormhole solutions.","Because the TOV balance is satisfied with zero gravitational force (constant redshift), the stability argument depends only on hydrostatic and anisotropic forces canceling; models satisfying that balance are in equilibrium.","NEC violation in all three models implies the wormhole throats must contain exotic matter, so the paper does not evade the usual energy-condition cost of traversability.","The requirement $\\alpha<0$ for asymptotic flatness ties the gravitational coupling sign to the existence of the solutions."],"supporting_citations":[{"why":"Supplies the Morris-Thorne metric and the throat, flaring-out, and asymptotic-flatness conditions used to define viable wormholes.","marker":"[3]"},{"why":"Extends the Morris-Thorne construction to wormhole spacetimes and time-machine cases, providing the metric class used in Eq. (3.1).","marker":"[4]"},{"why":"Gives the f(Q) action and field equations from which the wormhole field equations (4.2)-(4.4) are derived.","marker":"[40]"},{"why":"Supplies the linear $f(Q)=\\alpha Q$ model adopted in Sec. 4.1.","marker":"[42]"},{"why":"Supplies the varying Chaplygin gas and varying barotropic fluid equations of state used in Eqs. (5.1) and (6.1).","marker":"[44]"},{"why":"Supplies the generalized Chaplygin gas equation of state used in Eq. (5.6).","marker":"[45]"},{"why":"Provides the TOV hydrostatic equilibrium equation used for the stability analysis in Sec. 8.","marker":"[46]"}],"fun_headline_variants":["Dark energy EoS build traversable wormholes in f(Q)","Chaplygin gas wormholes in f(Q) gravity violate NEC","f(Q) gravity wormholes from dark energy equations","Traversable wormholes via dark energy in modified gravity"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The construction assumes the wormhole's radial pressure is exactly given by one of the three dark energy equations of state with the stated constants, and that $\\alpha$ must be negative for asymptotic flatness; if a different equation of state or a positive coupling were used, the derived shape functions and conclusions would no longer follow.","fun_headline_variants_meta":{"raw":{"variants":["Dark energy EoS build traversable wormholes in f(Q)","Chaplygin gas wormholes in f(Q) gravity violate NEC","f(Q) gravity wormholes from dark energy equations","Traversable wormholes via dark energy in modified gravity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000258,"raw_usage":{"total_tokens":1639,"prompt_tokens":1057,"completion_tokens":582,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":673,"completion_tokens_details":{"reasoning_tokens":513}},"tokens_in":673,"tokens_out":582,"duration_ms":6713,"temperature":1.0,"reasoning_tokens":513,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T19:59:57.452403+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Solve $b(r_0)=r_0$ for each shape function—(5.2), (5.7), and (6.2)—using the paper's stated parameters ($a=0.05$, $u=-4$, $B=1$, $c=0.09$ for WH1; $a=-1.2$, $B=1$, $c_1=10$ for WH2; $\\omega=-2$, $c_1=1$ for WH3) and check for a positive real root $r_0$ with $b'(r_0)<1$. If any model has no positive real throat radius or fails the flaring condition at that radius, the claimed traversable wormhole does not exist; separately, evaluating $\\rho+p_r$ at $r_0$ from (5.3)-(5.4), (5.8)-(5.9), and (6.3)-(6.4) would settle the NEC-violation claim.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Morris-Thorne metric and the throat, flaring-out, and asymptotic-flatness conditions used to define viable wormholes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Extends the Morris-Thorne construction to wormhole spacetimes and time-machine cases, providing the metric class used in Eq. (3.1)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the f(Q) action and field equations from which the wormhole field equations (4.2)-(4.4) are derived."},{"cited_title":"Hassan, S","cited_arxiv_id":null,"evidence_quote":"Supplies the linear $f(Q)=\\alpha Q$ model adopted in Sec. 4.1."},{"cited_title":"Elizalde and M","cited_arxiv_id":null,"evidence_quote":"Supplies the varying Chaplygin gas and varying barotropic fluid equations of state used in Eqs. (5.1) and (6.1)."},{"cited_title":"Bento, O","cited_arxiv_id":null,"evidence_quote":"Supplies the generalized Chaplygin gas equation of state used in Eq. (5.6)."}],"review_version":1}